question_answer

What is the resultant capacitance between  A and B ?

A)  51\[\mu F\]                                      

B)  102 \[\mu F\]

C)   204\[\mu F\]                                   

D)  408 \[\mu F\]

Correct Answer: C

Solution :

                 In the given circuit, two capacitors of \[20\mu F\]and \[5\mu F\] are connected in series and their resultant is connected in parallel to \[200\mu F\]capacitor.                 \[\therefore \]  \[\frac{1}{C}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}-\frac{1}{20}+\frac{1}{5}\]                 \[\frac{1}{C}=\frac{25}{20\times 5}\]                 \[{{C}_{s}}=\frac{20\times 5}{25}=4\,\mu F\] Resultant capacitance is \[{{C}_{p}}={{C}_{1}}+{{C}_{2}}\]                 \[=4+200=204\,\mu F\]